Multiscale Constrained Inversion Method for Direct Current Resistivity Tomography Based on Haar Wavelet Transform

Smoothness constrained inversion dominates the field of geoelectrical imaging. However, the resulting smooth images are unrealistic. In the absence of a priori underground information, the actual shape of the target geological structures are not well described. To address these limitations, we propose a multiscale inversion scheme. The inversion uses the wavelet transform method to convert the model parameters into Wavelet parameters. The Wavelet parameters are used as target values for the inversion. On this basis, different smoothness values were applied to different regions by controlling the feature parameter weights. Finally, the resistivity model was developed from the Wavelet parameters using the inverse wavelet transform. This study mainly considers the features of different depths and scales. By reducing the weight of the deep Wavelet parameters in the model objective function, the role of the data fitting objective function is enhanced, thereby improving the imaging of deep targets. Similarly, by reducing the weight of small-scale Wavelet parameters in the model objective function, the accuracy of the small-scale Wavelet parameters is improved. The small-scale Wavelet parameters correspond to the target boundary (fine or local) in the space domain, and hence, the actual shape of the target geological structures is better described. Compared with the traditional smoothness constrained inversion, the new method has a stronger boundary description effect on the target body. Numerical simulations have verified that different weights can improve the inversion performance. The feasibility of the algorithm was verified by using the sandbox test.